The 14-year-old was among 22 people who died when a suicide attacker detonated a nail bomb at an Ariana Grande concert in Manchester in May last year.
The teenager was the only Scot to die in the terror attack.
Her friend Laura MacIntyre was badly injured in the blast, but survived.
A report by Lord Bob Kerslake, commissioned by mayor of Greater Manchester Andy Burnham, found poor communications between the police and fire service meant the “valuable” assistance of fire crews was delayed by two hours and six minutes after the bombing, which left 22 dead and scores injured.
A statement issued by Eilidh’s parents Marion and Roddy, along with her sisters Shona and Laura, said: “As a family, we have considered Lord Kerslake’s report into the Manchester Arena tragedy and the recommendations contained in it.
“We greatly welcome and acknowledge the levels of well-deserved admiration for the numerous acts of heroism the report highlights.
“In particular, we wish to echo the praise awarded to individuals who made life and death decisions by keeping first responders at the arena.
“There is no doubt that these first responders provided the dying and injured with the vital comfort and aid at their time of most need.
“As we approach the first anniversary of her death, we continue to mourn our beloved Eilidh.
“We think of her in the same bright and positive light that shone from her during her short life with us as a daughter and as a sister.
“We also mourn all victims of atrocity.
“It is both right and proper that enquiries and reports should indicate where lessons can be learned in unprecedented situations like the Manchester tragedy.
“We must remain positive that any outcomes from such reports will help to educate and inform individuals, services and heads of service and enable them to act and react with confidence.
“Throughout this whole nightmare our respect and admiration for all the emergency services remains undiminished.”
Firefighters felt “ashamed” they could not help victims of the Manchester Arena terror attack more quickly, the north-west secretary of the Fire Brigade Union has said.
Mark Rowe told BBC Breakfast crews were “waiting to be deployed” after the bombing – some of them so close that they had heard the explosion – but “the order never came down from the top”.
The order comes after Dawn Docx, the interim chief fire officer of Greater Manchester Fire and Rescue Service, who made a public apology for firefighters being delayed by two hours before joining in the response.
Mr Rowe said: “Members were very angry that they weren’t being deployed to the scene.
“There was frustration. Members have talked about their embarrassment that they weren’t deployed and also feeling ashamed that they were prevented from doing anything that night.”